Index Exceeds array bounds - error on line 67 (x_3). Why is this error happening? How do I fix?

% Square Wave problem

% INPUTS

T = 5; % sec, Period of forcing function

F_o = 30; % N, amplitude

k = 1000; % N/m, spring stiffness

omega_n = 3; %rad/s, natural frequency

zeta = 0.1; % damping factor

num_terms = 5; % Number of terms for Fourier series

num_periods = 2;

del_t = T/100; % Time increment for results

%% CALCULATIONS

time = 0:del_t:num_periods*T;

omega_T = (2*pi) / T;

% Exact Forcing Function

for i = 1:length(time)

if time(i) <= T/2

F(i) = -F_o;

elseif time(i) <= T

F(i) = F_o;

elseif time(i) <= (3*T)/2

F(i) = -F_o;

else

F(i) = F_o;

end

end

% Fourier approximation of Forcing Function

for n = 1:num_terms

aj = zeros(n,1); % numerical integration

bj = [-120/pi; 0; -40/pi; 0; -24/pi];

end

for i = 1:length(time)

F_1(i) = aj(1)*cos(1*omega_T*time(i)) + bj(1)*sin(1*omega_T*time(i)) ;

F_2(i) = aj(2)*cos(2*omega_T*time(i)) + bj(2)*sin(2*omega_T*time(i)) ;

F_3(i) = aj(3)*cos(3*omega_T*time(i)) + bj(3)*sin(3*omega_T*time(i)) ;

F_4(i) = aj(4)*cos(4*omega_T*time(i)) + bj(4)*sin(4*omega_T*time(i)) ;

F_5(i) = aj(5)*cos(5*omega_T*time(i)) + bj(5)*sin(5*omega_T*time(i)) ;

F_Fourier = F_1 + F_2 + F_3 + F_4 + F_5;

end

% Response

r = zeros(1,5);

tan = zeros(1,5);

alpha = zeros(1,5);

x_1 = zeros(1,201);

x_3 = zeros(1,201);

x_5 = zeros(1,201);

for s = 1:num_terms

r(s) = s.*(omega_T / omega_n);

tan(s) = (2*zeta.*r) / (1-(r.^2));

alpha(s) = atan(tan(s));

end

X_1 = (bj(1) / k) * (1 / sqrt( ((1 - (r(1)^2))^2) + ((2*zeta*(r(1)))^2)));

% X_2 = (bj(2) / k) * (1 / sqrt( ((1 - (r(2)^2))^2) + ((2*zeta*(r(2)))^2)));

X_3 = (bj(3) / k) * (1 / sqrt( ((1 - (r(3)^2))^2) + ((2*zeta*(r(3)))^2)));

% X_4 = (bj(4) / k) * (1 / sqrt( ((1 - (r(4)^2))^2) + ((2*zeta*(r(4)))^2)));

X_5 = (bj(5) / k) * (1 / sqrt( ((1 - (r(5)^2))^2) + ((2*zeta*(r(5)))^2)));

x_1 = X_1*(sin(((s(1)*omega_T*time) - alpha(s(1)))));

% x_2 = X_2*(sin(((s(2)*omega_T*time) - alpha(s(2)))));

x_3 = X_3*sin(((s(3)*omega_T*time) - alpha(s(3))));

% x_4 = X_4*sin(((s(4)*omega_T*time) - alpha(s(4))));

x_5 = X_5*sin(((s(5)*omega_T*time) - alpha(s(5))));

x_p = x_1 + x_3 + x_5;

Answer 1

[Sarvani Panguluri]

Hi,

By reproducing your code,I have understood that the line causing the error is this

 x_3 = X_3*sin(((s(3)*omega_T*time) - alpha(s(3))));

Reason for this is , variable s is of type 1*1 double .So s(3) is not defined.This is because the variable s is defined in 'for' loop as index.When defined as index it increments from initial value to final value and only final value is stored in it at the end of loop execution.

You can add the following line after for loop

 for s = 1:num_terms
    r(s) = s.*(omega_T / omega_n);
    tan(s) = (2*zeta.*r) / (1-(r.^2));
    alpha(s) = atan(tan(s));    
 end
 s=1:num_terms;

Now s is 1*5 double of values [1,2,3,4,5].

Hope this helps!